Properties

Label 6038.2
Level 6038
Weight 2
Dimension 379764
Nonzero newspaces 4
Sturm bound 4557180

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Defining parameters

Level: \( N \) = \( 6038 = 2 \cdot 3019 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(4557180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6038))\).

Total New Old
Modular forms 1142313 379764 762549
Cusp forms 1136278 379764 756514
Eisenstein series 6035 0 6035

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6038))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
6038.2.a \(\chi_{6038}(1, \cdot)\) 6038.2.a.a 2 1
6038.2.a.b 54
6038.2.a.c 57
6038.2.a.d 69
6038.2.a.e 70
6038.2.c \(\chi_{6038}(239, \cdot)\) n/a 502 2
6038.2.e \(\chi_{6038}(9, \cdot)\) n/a 127006 502
6038.2.g \(\chi_{6038}(5, \cdot)\) n/a 252004 1004

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6038))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6038)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(3019))\)\(^{\oplus 2}\)